Trigonometry Practice Questions

JEE · Mathematics · 1493 free MCQs with instant results and detailed explanations.

1493

Total

358

Easy

648

Medium

487

Hard

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Topics in Trigonometry

Trigonometric Ratios 202

Identities 226

Compound Angles 186

Multiple and Sub-Multiple Angles 178

Trigonometric Equations 155

Inverse Trigonometric Functions 191

Properties of Triangles 202

Heights and Distances 153

Sample Questions from Trigonometry

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

In a right triangle, if the lengths of the opposite and adjacent sides are 3 and 4 respectively, what is the value of sin(θ)?

A. 3/5

B. 4/5

C. 5/3

D. 1/2

Show Answer & Explanation

Correct Answer: A

In a right triangle, sin(θ) is defined as the ratio of the length of the opposite side to the hypotenuse. The hypotenuse can be calculated as √(3² + 4²) = 5. Therefore, sin(θ) = opposite/hypotenuse = 3/5.

Easy

What is the ratio of sin(60°) to cos(30°)?

A. 1

B. √3

C. √2

D. 2

Show Answer & Explanation

Correct Answer: B

Both sin(60°) and cos(30°) equal √3/2, so their ratio is 1.

Easy

Which of the following is the correct value of cot(60°)?

A. 1/√3

B. 1/2

C. √3

D. 1

Show Answer & Explanation

Correct Answer: A

Cotangent is the reciprocal of tangent; since tan(60°) = √3, cot(60°) = 1/√3.

Medium

What is the value of tan(30°)?

A. 1/√3

B. √3

C. 2/√3

D. √2

Show Answer & Explanation

Correct Answer: A

Tan(30°) = 1/√3 is derived from the values of trigonometric functions for standard angles.

Medium

If sin x = 1/2, what are the possible values of x in the interval [0, 2π]?

A. π/6, 5π/6

B. π/3, 2π/3

C. 3π/2, 7π/6

D. 0, π

Show Answer & Explanation

Correct Answer: A

Sin x = 1/2 corresponds to angles π/6 and 5π/6 in the unit circle.

Medium

If cot A = 1/√3, what is the value of tan A?

A. √3

B. 1/√3

C. 3

D. √2

Show Answer & Explanation

Correct Answer: A

Tan A is the reciprocal of cot A, thus tan A = √3.

Medium

What is the value of sin(2θ) in terms of sin θ?

A. 2sin θ cos θ

B. sin² θ

C. 2sin² θ

D. sin θ + cos θ

Show Answer & Explanation

Correct Answer: A

The double angle formula for sine states that sin(2θ) = 2sin(θ)cos(θ).

Hard

If sec x = 13/5, what is the value of sin²x + cos²x?

A. 1

B. 0

C. 13/25

D. 5/13

Show Answer & Explanation

Correct Answer: A

Using the Pythagorean identity, sin²x + cos²x = 1 holds true for all angles x.

Hard

Calculate the value of sin 45° + cos 45°.

A. 1

B. √2

C. 2

D. √3

Show Answer & Explanation

Correct Answer: B

Both sin 45° and cos 45° equal to √2/2, so their sum is √2.

Q10

Hard

If tan²x + 1 = sec²x, what can you say about the angle x?

A. x is acute

B. x is obtuse

C. x is right

D. It can be any angle

Show Answer & Explanation

Correct Answer: A

This is a trigonometric identity valid for any angle, but typically refers to acute angles.

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Trigonometry — JEE Mathematics Practice Questions Online

This page contains 1493 practice MCQs for the chapter Trigonometry in JEE Mathematics. The questions are organized by difficulty — 358 easy, 648 medium, 487 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 8 topics, giving you comprehensive coverage of the entire chapter.